Small Oscillations about the equilibrium point:

AI Thread Summary
The equilibrium point for the potential function v(x) = (1/x^2) - (1/x) is determined to be at x=2. To find the frequency of small oscillations around this point, a Taylor series expansion of v(x) near x=2 is suggested. This approach allows for the approximation of the function, focusing on the quadratic term while neglecting higher-order terms. The resulting approximation can be treated as a simple harmonic oscillator, facilitating the calculation of the oscillation frequency. Understanding these steps is crucial for solving the problem effectively.
djames1009
Messages
9
Reaction score
0

Homework Statement



v(x)= (1/x^2) -(1/x) Find the frequency of small osciallations about the equilibrium point

Homework Equations





The Attempt at a Solution


I have so far worked out the equilibrium point is at x=2, to get this i differentiated v(x) and solved it, but could anybody help me on how i could work out the frequency of small oscialltions for this problem?
 
Physics news on Phys.org
It's been a while, but I think I know what's next. You need to approximate the function around the point x=2. Do a taylor series and hopefully the higher order terms are much smaller than the quadratic term. From here you can call it a simple harmonic oscillator.
 
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »

Similar threads

What is meant by small oscillations for this potential energy function?
Replies
2
Views
752
Angular frequency of the small oscillations of a pendulum
Replies
3
Views
2K
How Do You Calculate Oscillation Frequency for a Quadratic-Cubic Potential?
Replies
2
Views
1K
Understanding the generic nature of linearity in Physics
Replies
2
Views
937
Rotating simple harmonic oscillator
Replies
11
Views
1K
Why is a 1d conservative force approximately linearly related to position?
Replies
3
Views
638
For what values of total energy is the resulting motion periodic?
Replies
25
Views
933
Small oscillations of a simple pendulum placed on a moving block
2
Replies
73
Views
4K
A charge inside a ring, small oscillation
Replies
2
Views
1K
Two spring-coupled masses in an electric field (one of the masses is charged)
Replies
1
Views
845

Hot Threads

Recent Insights

Back
Top